Question

A flashlight has 8 batteries, 3 of which are defective. If 3 are selected at random without replacement, find the probability that all of them are defective. Enter your answer as a fraction or a decimal rounded to 3 decimal places. The probability of getting all of them defective batteries is___

Answer 1

The probability that all three selected batteries are defective is 1/56, approximately 0.018.,

Step-by-step explanation:

To find the probability that all three selected batteries are defective, we need to determine the number of ways to choose 3 defective batteries out of the 3 defective ones and then divide it by the total number of ways to choose 3 batteries from the 8 available.

The probability can be calculated as:

P(all 3 defective) = (number of ways to choose 3 defective batteries) / (number of ways to choose 3 batteries)

The number of ways to choose 3 defective batteries out of 3 is 1, and the number of ways to choose 3 batteries out of 8 is the combination of 8 choose 3, which is calculated as:

8C3 = 8! / (3!(8-3)!) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56

Therefore, the probability that all three selected batteries are defective is 1/56, which is approximately 0.018 when rounded to 3 decimal places.